Question: Solve for $t$, $ -\dfrac{10}{2t - 3} = -\dfrac{t - 5}{10t - 15} - \dfrac{3}{2t - 3} $
Solution: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $2t - 3$ $10t - 15$ and $2t - 3$ The common denominator is $10t - 15$ To get $10t - 15$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ -\dfrac{10}{2t - 3} \times \dfrac{5}{5} = -\dfrac{50}{10t - 15} $ The denominator of the second term is already $10t - 15$ , so we don't need to change it. To get $10t - 15$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ -\dfrac{3}{2t - 3} \times \dfrac{5}{5} = -\dfrac{15}{10t - 15} $ This give us: $ -\dfrac{50}{10t - 15} = -\dfrac{t - 5}{10t - 15} - \dfrac{15}{10t - 15} $ If we multiply both sides of the equation by $10t - 15$ , we get: $ -50 = -t + 5 - 15$ $ -50 = -t - 10$ $ -40 = -t $ $ t = 40$